Method for characterizing distortions in a lithographic process, lithographic apparatus, lithographic cell and computer program

ABSTRACT

A method of characterizing distortions in a lithographic process, and associated apparatuses. The method includes obtaining measurement data corresponding to a plurality of measurement locations on a substrate, the measurement data comprising measurements performed on a plurality of substrates, and comprising one or more measurements performed on one or more of the substrates for each of the measurement locations. For each of the measurement locations, a first quality value representing a quality metric and a noise value representing a noise metric is determined from the measurements performed at that measurement location. A plurality of distortion parameters is determined, each distortion parameter configured to characterize a systematic distortion in the quality metric and a statistical significance of the distortion parameters from the first quality value and from the noise value is determined. Systematic distortion is parameterized from the distortion parameters determined to be statistically significant.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is the U.S. national phase entry of PCT patentapplication no. PCT/EP2017/054017, which was filed on Feb. 22, 2017,which claims the benefit of priority of European patent application no.16158667.2 which was filed on Mar. 4, 2016, and which is incorporatedherein in its entirety by reference.

BACKGROUND Field of the Invention

The present invention relates to methods and apparatus for metrologyusable, for example, in the manufacture of devices by lithographictechniques and to methods of manufacturing devices using lithographictechniques.

Background Art

A lithographic apparatus is a machine that applies a desired patternonto a substrate, usually onto a target portion of the substrate. Alithographic apparatus can be used, for example, in the manufacture ofintegrated circuits (ICs). In that instance, a patterning device, whichis alternatively referred to as a mask or a reticle, may be used togenerate a circuit pattern to be formed on an individual layer of theIC. This pattern can be transferred onto a target portion (e.g.,including part of, one, or several dies) on a substrate (e.g., a siliconwafer). Transfer of the pattern is typically via imaging onto a layer ofradiation-sensitive material (resist) provided on the substrate. Ingeneral, a single substrate will contain a network of adjacent targetportions that are successively patterned. In lithographic processes, itis desirable frequently to make measurements of the structures created,e.g., for process control and verification. Various tools for makingsuch measurements are known, including scanning electron microscopes,which are often used to measure critical dimension (CD), and specializedtools to measure overlay, a measure of the accuracy of alignment of twolayers in a device. Overlay may be described in terms of the degree ofmisalignment between the two layers, for example reference to a measuredoverlay of 1 nm may describe a situation where two layers are misalignedby 1 nm.

Recently, various forms of scatterometers have been developed for use inthe lithographic field. These devices direct a beam of radiation onto atarget and measure one or more properties of the scatteredradiation—e.g., intensity at a single angle of reflection as a functionof wavelength; intensity at one or more wavelengths as a function ofreflected angle; or polarization as a function of reflected angle—toobtain a “spectrum” from which a property of interest of the target canbe determined. Determination of the property of interest may beperformed by various techniques: e.g., reconstruction of the target byiterative approaches such as rigorous coupled wave analysis or finiteelement methods; library searches; and principal component analysis.

The targets used by conventional scatterometers are relatively large,e.g., 40 μm by 40 μm, gratings and the measurement beam generates a spotthat is smaller than the grating (i.e., the grating is underfilled).This simplifies mathematical reconstruction of the target as it can beregarded as infinite. However, in order to reduce the size of thetargets, e.g., to 10 μm by 10 μm or less, e.g., so they can bepositioned in amongst product features, rather than in the scribe lane,metrology has been proposed in which the grating is made smaller thanthe measurement spot (i.e., the grating is overfilled). Typically suchtargets are measured using dark field scatterometry in which the zerothorder of diffraction (corresponding to a specular reflection) isblocked, and only higher orders processed. Examples of dark fieldmetrology can be found in international patent applications WO2009/078708 and WO 2009/106279 which documents are hereby incorporatedby reference in their entirety. Further developments of the techniquehave been described in patent publications US20110027704A,US20110043791A and US20120242970A. The contents of all theseapplications are also incorporated herein by reference.Diffraction-based overlay using dark-field detection of the diffractionorders enables overlay measurements on smaller targets. These targetscan be smaller than the illumination spot and may be surrounded byproduct structures on a wafer. Targets can comprise multiple gratingswhich can be measured in one image.

In the known metrology technique, overlay measurement results areobtained by measuring an overlay target twice under certain conditions,while either rotating the overlay target or changing the illuminationmode or imaging mode to obtain separately the −1^(st) and the +1^(st)diffraction order intensities. The intensity asymmetry, a comparison ofthese diffraction order intensities, for a given overlay target providesa measurement of target asymmetry, that is asymmetry in the target. Thisasymmetry in the overlay target can be used as an indicator of overlayerror (undesired misalignment of two layers).

Semiconductor processing equipment (e.g., lithography, etch, bake,polish and anneal) can introduce distortions in patterning performance(overlay, CD, Focus etc.) which may be characterized by a “fingerprint”describing the distortions in terms of a number of distortionparameters. Depending on the model used and the number of measurementsmade, the number of distortion parameters can vary, for example, betweena few tens to over a thousand. The number of distortion parameters usedto model the fingerprint is a balance between the time it takes to makesufficient measurements to sufficiently suppress noise and providingsufficient distortion parameters to properly describe the fingerprint.It would be desirable to provide a more efficient parameterization of afingerprint for process corrections.

SUMMARY OF THE INVENTION

The invention in a first aspect provides a method of characterizingdistortions in a lithographic process, said method comprising:

-   -   obtaining measurement data corresponding to a plurality of        measurement locations on a substrate, said measurement data        comprising measurements performed on a plurality of substrates,        and comprising one or more measurements performed on one or more        of said substrates for each of said measurement locations;    -   determining for each of said measurement locations a first        quality value representing a quality metric and a noise value        representing a noise metric from the measurements performed at        that measurement location;    -   determining a plurality of distortion parameters, each        distortion parameter being configured to characterize a        systematic distortion in said quality metric;    -   determining a statistical significance of said distortion        parameters from said first quality value and from said noise        value; and    -   parameterizing the systematic distortion from the distortion        parameters determined to be statistically significant.

The invention further provides a lithographic apparatus or lithographiccell operable to perform the method of the first aspect.

The invention further provides a computer program comprising processorreadable instructions which, when run on suitable processor controlledapparatus, cause the processor controlled apparatus to perform themethod of the first aspect, and a computer program carrier comprisingsuch a computer program. The processor controlled apparatus may comprisethe aforementioned lithographic apparatus or lithographic cell.

Further features and advantages of the invention, as well as thestructure and operation of various embodiments of the invention, aredescribed in detail below with reference to the accompanying drawings.It is noted that the invention is not limited to the specificembodiments described herein. Such embodiments are presented herein forillustrative purposes only. Additional embodiments will be apparent topersons skilled in the relevant art(s) based on the teachings containedherein.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the invention will now be described, by way of exampleonly, with reference to the accompanying drawings in which:

FIG. 1 depicts a lithographic apparatus together with other apparatusesforming a production facility for semiconductor devices;

FIG. 2 comprises (a) a schematic diagram of a dark field scatterometerfor use in measuring targets using a first pair of illuminationapertures, (b) a detail of diffraction spectrum of a target grating fora given direction of illumination;

FIG. 3 is a flowchart describing a method for a modelling and correctionstrategy according to an embodiment of the invention.

DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS

Before describing embodiments of the invention in detail, it isinstructive to present an example environment in which embodiments ofthe present invention may be implemented.

FIG. 1 at 200 shows a lithographic apparatus LA as part of an industrialfacility implementing a high-volume, lithographic manufacturing process.In the present example, the manufacturing process is adapted for themanufacture of semiconductor products (integrated circuits) onsubstrates such as semiconductor wafers. The skilled person willappreciate that a wide variety of products can be manufactured byprocessing different types of substrates in variants of this process.The production of semiconductor products is used purely as an examplewhich has great commercial significance today.

Within the lithographic apparatus (or “litho tool” 200 for short), ameasurement station MEA is shown at 202 and an exposure station EXP isshown at 204. A control unit LACU is shown at 206. In this example, eachsubstrate visits the measurement station and the exposure station tohave a pattern applied. In an optical lithographic apparatus, forexample, a projection system is used to transfer a product pattern froma patterning device MA onto the substrate using conditioned radiationand a projection system. This is done by forming an image of the patternin a layer of radiation-sensitive resist material.

The term “projection system” used herein should be broadly interpretedas encompassing any type of projection system, including refractive,reflective, catadioptric, magnetic, electromagnetic and electrostaticoptical systems, or any combination thereof, as appropriate for theexposure radiation being used, or for other factors such as the use ofan immersion liquid or the use of a vacuum. The patterning MA device maybe a mask or reticle, which imparts a pattern to a radiation beamtransmitted or reflected by the patterning device. Well-known modes ofoperation include a stepping mode and a scanning mode. As is well known,the projection system may cooperate with support and positioning systemsfor the substrate and the patterning device in a variety of ways toapply a desired pattern to many target portions across a substrate.Programmable patterning devices may be used instead of reticles having afixed pattern. The radiation for example may include electromagneticradiation in the deep ultraviolet (DUV) or extreme ultraviolet (EUV)wavebands. The present disclosure is also applicable to other types oflithographic process, for example imprint lithography and direct writinglithography, for example by electron beam.

The lithographic apparatus control unit LACU which controls all themovements and measurements of various actuators and sensors to receivesubstrates W and reticles MA and to implement the patterning operations.LACU also includes signal processing and data processing capacity toimplement desired calculations relevant to the operation of theapparatus. In practice, control unit LACU will be realized as a systemof many sub-units, each handling the real-time data acquisition,processing and control of a subsystem or component within the apparatus.

Before the pattern is applied to a substrate at the exposure stationEXP, the substrate is processed in at the measurement station MEA sothat various preparatory steps may be carried out. The preparatory stepsmay include mapping the surface height of the substrate using a levelsensor and measuring the position of alignment marks on the substrateusing an alignment sensor. The alignment marks are arranged nominally ina regular grid pattern. However, due to inaccuracies in creating themarks and also due to deformations of the substrate that occurthroughout its processing, the marks deviate from the ideal grid.Consequently, in addition to measuring position and orientation of thesubstrate, the alignment sensor in practice must measure in detail thepositions of many marks across the substrate area, if the apparatus isto print product features at the correct locations with very highaccuracy. The apparatus may be of a so-called dual stage type which hastwo substrate tables, each with a positioning system controlled by thecontrol unit LACU. While one substrate on one substrate table is beingexposed at the exposure station EXP, another substrate can be loadedonto the other substrate table at the measurement station MEA so thatvarious preparatory steps may be carried out. The measurement ofalignment marks is therefore very time-consuming and the provision oftwo substrate tables enables a substantial increase in the throughput ofthe apparatus. If the position sensor IF is not capable of measuring theposition of the substrate table while it is at the measurement stationas well as at the exposure station, a second position sensor may beprovided to enable the positions of the substrate table to be tracked atboth stations. Lithographic apparatus LA may for example is of aso-called dual stage type which has two substrate tables and twostations—an exposure station and a measurement station—between which thesubstrate tables can be exchanged.

Within the production facility, apparatus 200 forms part of a “lithocell” or “litho cluster” that contains also a coating apparatus 208 forapplying photosensitive resist and other coatings to substrates W forpatterning by the apparatus 200. At an output side of apparatus 200, abaking apparatus 210 and developing apparatus 212 are provided fordeveloping the exposed pattern into a physical resist pattern. Betweenall of these apparatuses, substrate handling systems take care ofsupporting the substrates and transferring them from one piece ofapparatus to the next. These apparatuses, which are often collectivelyreferred to as the track, are under the control of a track control unitwhich is itself controlled by a supervisory control system SCS, whichalso controls the lithographic apparatus via lithographic apparatuscontrol unit LACU. Thus, the different apparatus can be operated tomaximize throughput and processing efficiency. Supervisory controlsystem SCS receives recipe information R which provides in great detaila definition of the steps to be performed to create each patternedsubstrate.

Once the pattern has been applied and developed in the litho cell,patterned substrates 220 are transferred to other processing apparatusessuch as are illustrated at 222, 224, 226. A wide range of processingsteps is implemented by various apparatuses in a typical manufacturingfacility. For the sake of example, apparatus 222 in this embodiment isan etching station, and apparatus 224 performs a post-etch annealingstep. Further physical and/or chemical processing steps are applied infurther apparatuses, 226, etc. Numerous types of operation can berequired to make a real device, such as deposition of material,modification of surface material characteristics (oxidation, doping, ionimplantation etc.), chemical-mechanical polishing (CMP), and so forth.The apparatus 226 may, in practice, represent a series of differentprocessing steps performed in one or more apparatuses.

As is well known, the manufacture of semiconductor devices involves manyrepetitions of such processing, to build up device structures withappropriate materials and patterns, layer-by-layer on the substrate.Accordingly, substrates 230 arriving at the litho cluster may be newlyprepared substrates, or they may be substrates that have been processedpreviously in this cluster or in another apparatus entirely. Similarly,depending on the required processing, substrates 232 on leavingapparatus 226 may be returned for a subsequent patterning operation inthe same litho cluster, they may be destined for patterning operationsin a different cluster, or they may be finished products to be sent fordicing and packaging.

Each layer of the product structure requires a different set of processsteps, and the apparatuses 226 used at each layer may be completelydifferent in type. Further, even where the processing steps to beapplied by the apparatus 226 are nominally the same, in a largefacility, there may be several supposedly identical machines working inparallel to perform the step 226 on different substrates. Smalldifferences in set-up or faults between these machines can mean thatthey influence different substrates in different ways. Even steps thatare relatively common to each layer, such as etching (apparatus 222) maybe implemented by several etching apparatuses that are nominallyidentical but working in parallel to maximize throughput. In practice,moreover, different layers require different etch processes, for examplechemical etches, plasma etches, according to the details of the materialto be etched, and special requirements such as, for example, anisotropicetching.

The previous and/or subsequent processes may be performed in otherlithography apparatuses, as just mentioned, and may even be performed indifferent types of lithography apparatus. For example, some layers inthe device manufacturing process which are very demanding in parameterssuch as resolution and overlay may be performed in a more advancedlithography tool than other layers that are less demanding. Thereforesome layers may be exposed in an immersion type lithography tool, whileothers are exposed in a ‘dry’ tool. Some layers may be exposed in a toolworking at DUV wavelengths, while others are exposed using EUVwavelength radiation.

In order that the substrates that are exposed by the lithographicapparatus are exposed correctly and consistently, it is desirable toinspect exposed substrates to measure properties such as overlay errorsbetween subsequent layers, line thicknesses, critical dimensions (CD),etc. Accordingly a manufacturing facility in which litho cell LC islocated may also include one or more metrology systems. The metrologysystems may include a stand-alone metrology apparatus MET 240 and/or anintegrated metrology apparatus IM 207. The stand-alone metrologyapparatus MET 240 receives some or all of the substrates W that havebeen processed in the litho cell for performing measurements offline.The integrated metrology apparatus IM 207 performs inline measurementsand is integrated into the track to receive and measure some or all ofthe substrates W immediately after exposure. Metrology results areprovided directly or indirectly to the supervisory control system (SCS)238. If errors are detected, adjustments may be made to exposures ofsubsequent substrates, especially if the metrology can be done soon andfast enough that other substrates of the same batch are still to beexposed.

A common example of a metrology apparatus in a modern lithographicproduction facility is a scatterometer, for example an angle-resolvedscatterometer or a spectroscopic scatterometer, and it may normally beapplied to measure properties of the developed substrates at 220 priorto etching in the apparatus 222. Using stand-alone metrology apparatus240 and/or integrated metrology apparatus 207, it may be determined, forexample, that important performance parameters such as overlay orcritical dimension (CD) do not meet specified accuracy requirements inthe developed resist. Prior to the etching step, the opportunity existsto strip the developed resist and reprocess the substrates 220 throughthe litho cluster. As is also well known, the metrology results 242 fromthe apparatus 240 can be used to maintain accurate performance of thepatterning operations in the litho cluster, by supervisory controlsystem SCS and/or control unit LACU 206 making small adjustments overtime, thereby minimizing the risk of products being madeout-of-specification, and requiring re-work. Of course, metrologyapparatus 240 and/or other metrology apparatuses (not shown) can beapplied to measure properties of the processed substrates 232, 234, andincoming substrates 230.

A metrology apparatus is shown in FIG. 2(a). The stand-alone metrologyapparatus 240 and/or the integrated metrology apparatus 207 may comprisesuch a metrology apparatus, for example, or any other suitable metrologyapparatus. A target T and diffracted rays of measurement radiation usedto illuminate the target are illustrated in more detail in FIG. 2(b).The metrology apparatus illustrated is of a type known as a dark fieldmetrology apparatus. The metrology apparatus may be a stand-alone deviceor incorporated in either the lithographic apparatus LA, e.g., at themeasurement station, or the lithographic cell LC. An optical axis, whichhas several branches throughout the apparatus, is represented by adotted line O. In this apparatus, light emitted by source 11 (e.g., axenon lamp) is directed onto substrate W via a beam splitter 15 by anoptical system comprising lenses 12, 14 and objective lens 16. Theselenses are arranged in a double sequence of a 4F arrangement. Adifferent lens arrangement can be used, provided that it still providesa substrate image onto a detector, and simultaneously allows for accessof an intermediate pupil-plane for spatial-frequency filtering.Therefore, the angular range at which the radiation is incident on thesubstrate can be selected by defining a spatial intensity distributionin a plane that presents the spatial spectrum of the substrate plane,here referred to as a (conjugate) pupil plane. In particular, this canbe done by inserting an aperture plate 13 of suitable form betweenlenses 12 and 14, in a plane which is a back-projected image of theobjective lens pupil plane. In the example illustrated, aperture plate13 has different forms, labeled 13N and 13S, allowing differentillumination modes to be selected. The illumination system in thepresent examples forms an off-axis illumination mode. In the firstillumination mode, aperture plate 13N provides off-axis from a directiondesignated, for the sake of description only, as ‘north’. In a secondillumination mode, aperture plate 13S is used to provide similarillumination, but from an opposite direction, labeled ‘south’. Othermodes of illumination are possible by using different apertures. Therest of the pupil plane is desirably dark as any unnecessary lightoutside the desired illumination mode will interfere with the desiredmeasurement signals.

As shown in FIG. 2(b), target T is placed with substrate W normal to theoptical axis O of objective lens 16. The substrate W may be supported bya support (not shown). A ray of measurement radiation I impinging ontarget T from an angle off the axis O gives rise to a zeroth order ray(solid line 0) and two first order rays (dot-chain line +1 and doubledot-chain line −1). It should be remembered that with an overfilledsmall target, these rays are just one of many parallel rays covering thearea of the substrate including metrology target T and other features.Since the aperture in plate 13 has a finite width (necessary to admit auseful quantity of light, the incident rays I will in fact occupy arange of angles, and the diffracted rays 0 and +1/−1 will be spread outsomewhat. According to the point spread function of a small target, eachorder +1 and −1 will be further spread over a range of angles, not asingle ideal ray as shown. Note that the grating pitches of the targetsand the illumination angles can be designed or adjusted so that thefirst order rays entering the objective lens are closely aligned withthe central optical axis. The rays illustrated in FIGS. 2(a) and 3(b)are shown somewhat off axis, purely to enable them to be more easilydistinguished in the diagram.

At least the 0 and +1 orders diffracted by the target T on substrate Ware collected by objective lens 16 and directed back through beamsplitter 15. Returning to FIG. 2(a), both the first and secondillumination modes are illustrated, by designating diametricallyopposite apertures labeled as north (N) and south (S). When the incidentray I of measurement radiation is from the north side of the opticalaxis, that is when the first illumination mode is applied using apertureplate 13N, the +1 diffracted rays, which are labeled +1(N), enter theobjective lens 16. In contrast, when the second illumination mode isapplied using aperture plate 13S the −1 diffracted rays (labeled −1(S))are the ones which enter the lens 16.

A second beam splitter 17 divides the diffracted beams into twomeasurement branches. In a first measurement branch, optical system 18forms a diffraction spectrum (pupil plane image) of the target on firstsensor 19 (e.g. a CCD or CMOS sensor) using the zeroth and first orderdiffractive beams. Each diffraction order hits a different point on thesensor, so that image processing can compare and contrast orders. Thepupil plane image captured by sensor 19 can be used for focusing themetrology apparatus and/or normalizing intensity measurements of thefirst order beam. The pupil plane image can also be used for manymeasurement purposes such as reconstruction.

In the second measurement branch, optical system 20, 22 forms an imageof the target T on sensor 23 (e.g. a CCD or CMOS sensor). In the secondmeasurement branch, an aperture stop 21 is provided in a plane that isconjugate to the pupil-plane. Aperture stop 21 functions to block thezeroth order diffracted beam so that the image of the target formed onsensor 23 is formed only from the −1 or +1 first order beam. The imagescaptured by sensors 19 and 23 are output to processor PU which processesthe image, the function of which will depend on the particular type ofmeasurements being performed. Note that the term ‘image’ is used here ina broad sense. An image of the grating lines as such will not be formed,if only one of the −1 and +1 orders is present.

The particular forms of aperture plate 13 and field stop 21 shown inFIG. 2 are purely examples. In another embodiment of the invention,on-axis illumination of the targets is used and an aperture stop with anoff-axis aperture is used to pass substantially only one first order ofdiffracted light to the sensor. In yet other embodiments, 2^(nd), 3^(rd)and higher order beams (not shown in FIG. 2) can be used inmeasurements, instead of or in addition to the first order beams.

In order to make the measurement radiation adaptable to these differenttypes of measurement, the aperture plate 13 may comprise a number ofaperture patterns formed around a disc, which rotates to bring a desiredpattern into place. Note that aperture plate 13N or 13S can only be usedto measure gratings oriented in one direction (X or Y depending on theset-up). For measurement of an orthogonal grating, rotation of thetarget through 90° and 270° might be implemented. The use of these, andnumerous other variations and applications of the apparatus aredescribed in prior published applications, mentioned above.

Semiconductor processing tools can introduce variations that can lead toa process fingerprint, which characterizes the tool's imperfections.Such imperfections result in process distortions which cause (forexample) overlay errors. A “fingerprint” is a systematic distortion, ordeviation from ideal, in a metric, such as e.g., overlay, criticaldimension, focus or dose. There may be a physical reason for thefingerprint, e.g., the geometry of a particular tool or apparatus. Thisdeviation is systematic in the physical sense insofar as the variationwill repeat over multiple instances (e.g., multiple fields, substrates,lots and/or times), although there can be a slow variation betweendifferent instances due to, for example, wear or other changes in thetool over time. The fingerprint metrics (as measured) vary as a functionof another set of (known) distortion parameters and therefore can becharacterized by these distortion parameters.

The most accurate process correction mechanism in lithographicprocessing commonly characterizes the fingerprints directly in terms ofcorrectable distortion parameters of the lithographic process tool. Oneexample is the corrections per exposure (CPE) technique which appliesintra-field corrections per exposure. In this technique, correctabledistortion parameters are measured on a processed wafer for each exposedfield. These measured distortion parameters are than used to correct thefingerprint by applying appropriate corrections for each exposed fieldin subsequent lots, using all the correction capabilities (degrees offreedom) of the lithographic apparatus. A drawback of such methods ofdirectly fitting correctable distortion parameters to fingerprintmeasurements is that it can be highly inefficient. The number ofmeasurements required for correction is not a function of thefingerprint characteristics, but of the correction capabilities of thelithographic process tool. Until recently, the number of correctabledistortion parameters was relatively few, so this was not a significantproblem. Current tools have much greater correction capabilities (in theregion of thousands of distortion parameters, e.g., between 1200 and6000 distortion parameters depending on the apparatus), and therefore afingerprint defined in terms of correctable distortion parameters hasbecome unwieldy and requires a large number of measurements to obtainwith sufficient noise suppression.

An alternative to CPE is a higher order process correction (HOPC) modelin which only a subset of all fields and/or a subset of overlay targetsper field are measured and a polynomial fitted to the measurements, thepolynomial then being used to estimate overlay values for unmeasuredfields. The HOPC model uses approximately 50 distortion parameters whichare determined and updated each lot. Therefore, in contrast to CPEcontrol, HOPC control per lot uses an insufficient number of distortionparameters to accurately capture the fingerprint.

More recently, it has become possible to choose a model with a morebalanced number of distortion parameters, between the approximately 50distortion parameters of HOPC and approximately 1200 distortionparameters of CPE, enabling run-to-run control each lot with moreoptimal fingerprint capture and noise suppression. Typically, thisbalance is such that the fingerprint capture aspect can be improvedupon. Very high resolution fingerprints or fingerprints with afield-to-field discontinuity can be better captured, but only when thereis sufficient data to average out noise.

It is therefore proposed to use a modelling and correction strategywhere the resolution is dynamically adaptive depending on the amount ofmeasurement data obtained and/or the quality of this measurement data.The model resolution will increase with the number of model distortionparameters that can be estimated with sufficient precision. In this wayan optimal balance between fingerprint capture and noise suppression ismaintained.

FIG. 3 is a flowchart of the steps of a method for a modelling andcorrection strategy according to an exemplary embodiment. The steps areas follows, and are then described in greater detail thereafter:

-   -   300—Measure substrate;    -   310—Determine quality metric (e.g., overlay offset) per        position;    -   320—Determine noise metric per position;    -   330—Determine which distortion parameters can be calculated with        sufficient accuracy;    -   340—Determine corrections.

At step 300, measurements are made using a metrology apparatus. A full,dense substrate measurement required for CPE is too slow commercially tobe performed on a per-wafer basis. Therefore, in an embodiment, it isproposed that only a subset of the total measurement locations aremeasured per substrate, with a different subset of measurement locationsbeing measured on each substrate and/or each lot. In this way, over thecourse of a number of substrates or a number of lots, most or all of themeasurement locations will be measured at least once. The measurementlocations included in each subset may be sampled randomly (orpseudo-randomly), may follow set patterns, or the sampling may be basedon a distortion parameter value and/or one or models (such as afingerprint model). Such a sampling method will take multiplesubstrates, and possibly multiple lots, to obtain one or more fullymeasured substrates (a “fully measured substrate” in this contextmeaning measurement data comprising at least one measurement for eachmeasurement location, the measurement data comprising measurementsperformed on a number of different substrates in actuality).Furthermore, different measurement locations will not necessarily bemeasured an equal number of times.

At step 310, a first quality value representing a quality metric isdetermined per measurement location. This first quality value may becalculated as a moving average (e.g., mean) as more measurements at eachmeasurement location are made. The quality metric in the describedembodiment is overlay offset, although it may comprise another metricsuch as critical dimension, focus or dose, for example.

At step 320, a noise value representing the random variation in themeasurements (or other noise metric) per measurement location isdetermined. This noise value may comprise the standard deviation of themeasurements. This random variation may be calculated as a movingaverage as more measurements at each measurement location are made.

At step 330, using the results of steps 310 and 320, it is determinedwhich distortion parameters of one or more (e.g., higher resolution)estimation models can be determined with a sufficient statisticalsignificance. This may be achieved by determining from the results ofsteps 310 and 320, a substrate map indicating the average (e.g., mean)overlay offset and a confidence interval. In general, (for a givenconfidence level) the more times that a measurement location is actuallymeasured and/or the less random variation (smaller standard deviation)there is in the measured data, the smaller the confidence interval willbe for that measurement location. More specifically, the confidenceinterval defines a range of observed overlay values which is likely tocomprise the actual overlay value for that measurement location. Thelevel of confidence that the actual overlay value is within theconfidence interval is the confidence level, which can in theory be setat any value. Any appropriate confidence level may be chosen, forexample any value greater than 85%, greater than 90%, greater than 95%or greater than 99%. In an embodiment, the confidence level may be 90%,or at the 2-sigma (95%) or at 3-sigma level (99.7%). The significancelevel is a complement of the confidence level, i.e., a confidence levelof 90% yields a significance level of 10%.

In an embodiment, for each measurement location, the difference of theoverlay offset values estimated according to one (or more) (e.g., lowerresolution) models (second quality values) and the overlay offset valuesas estimated from actual measurements at that measurement location(first quality values) is calculated. The difference may be thought of,for example, as the difference between overlay offset values from alower resolution model and from a CPE model. It is then determinedwhether this difference (if any) is statistically significant. Thisdetermination may be made by determining whether this difference isoutside of the confidence interval as determined for that location. Ifthe difference is outside of the confidence interval, then it may beconsidered to be statistically significant, otherwise not. As the numberof measurement locations increases for which there is calculated astatistically significant difference, the resolution of the model usedto describe the fingerprint in an iteration can also be increased, whileensuring noise is sufficiently suppressed. By way of specific example,the lower resolution model may be a higher-order estimation model withbetween 40 and 100 distortion parameters (e.g., between 50 and 80distortion parameters) and the higher resolution model may be a CPEestimation model with more than 500 distortion parameters or more than1000 distortion parameters (e.g., in the region of 1200 distortionparameters), or more than 3000 distortion parameters or more than 5000distortion parameters.

To provide a specific example for illustration, an overlay offset valuemay be estimated using a low resolution model at a measurement location.The overlay offset may also have been actually measured twice at themeasurement location using a metrology tool. As with any measurement,the measured values will be subject to noise (random variation) andtherefore may differ. The mean of the measured values can be calculated,as can a measure of the random variation (e.g., standard deviation) andconfidence interval. The difference between the overlay offset valueestimated using the low resolution model and the overlay offset valueestimated using overlay offset values directly obtained from actualmeasurements at that location (e.g. using a high resolution model or CPEmodel) is calculated. If this difference lies outside of the confidenceinterval, then it is considered statistically significant and the CPEmodel is considered to provide a statistically significantly improvedestimate over the low resolution model and as such the correspondinghigh resolution distortion parameters can be used to describe thefingerprint for this location. If the difference lies within theconfidence interval, then it may be attributed to noise and the lowerresolution distortion parameters used (the lower resolution distortionparameters are also used when there is no difference). As moremeasurements are made at that location, the confidence interval willbecome smaller and therefore it becomes more likely that the determineddifference in offset values between the models is determined to bestatistically significant, meaning that more high resolution distortionparameters can be used to describe the fingerprint.

The fingerprint may be described according to one of a number ofpredetermined models, with the model chosen which best fits thestatistically significant higher resolution distortion parameters andthe remaining lower resolution distortion parameters. Alternatively, themodelled fingerprint may be varied on a per-distortion parameter basis,with each higher resolution distortion parameter that is determined tobe statistically significant included in the modelled fingerprint. As afurther alternative, a combination of these two previous alternativescan be used, where the best fitting model of a number of predeterminedmodels is selected and then further varied on a per-parameter basis toimprove the fit further. In this way, the resultant fingerprint will bedescribed with more distortion parameters as each distortion parameteris determined with sufficient statistical significance.

At step 340, the resultant fingerprint is used to calculate correctionsusing some, most or all degrees of freedom of the lithographic apparatuscorresponding to the model distortion parameters describing thefingerprint for that iteration.

This method may then be repeated such that the modelled fingerprint andconsequently the calculated corrections are updated iteratively. Eachiteration may be performed per number of measurements, per substratemeasured, per number of substrates measured, per lot, or per fullymeasured substrate for example.

The sampling at step 300 is described as optionally being based on adistortion parameter value. In an embodiment, the distortion parametervalue may be the difference between an overlay offset and a statisticalprecision limit. In this way, the precision at a location where anoverlay offset value is close to a statistical precision limit can beadaptively optimized using the metrology data. For example, where thedifference between the overlay offset value determined using a lowerresolution model and the overly offset value determined directly frommeasurements for that location is within the confidence interval forthis location, but close to the confidence limit, then this location maybe chosen for a further measurement on the next substrate (or so). Closeto the confidence limit may be within a percentage value of theconfidence limit. Or else, it may be determined that measurements foreach iteration comprise measurements of one or more locations for whichthis difference is closest to the corresponding confidence limit. Inthis way, the overlay offset value from the measured data close to theconfidence limit but within the confidence interval may be taken outsideof the confidence interval and therefore be considered statisticallysignificant, enabling an increase in the fingerprint resolution.

In the above description, the quality metric comprises overlay offset.However, this is only one example of a quality metric which benefitsfrom corrections determined using the concepts described herein. Otherquality metrics which can be used in place of overly offset in themethods described above include critical dimension, focus or dose.

The concepts proposed herein provide an adaptive resolution control,based on statistical significance of overlay offsets in measured dataand dynamic sampling to cover the full substrate for control. Anadditional benefit is that the user gets insight in measured offsets andvariation on full substrate coverage.

While the targets described above are metrology targets specificallydesigned and formed for the purposes of measurement, in otherembodiments, properties may be measured on targets which are functionalparts of devices formed on the substrate. Many devices have regular,grating-like structures. The terms ‘target grating’ and ‘target’ as usedherein do not require that the structure has been provided specificallyfor the measurement being performed.

In association with the physical grating structures of the targets asrealized on substrates and patterning devices, an embodiment may includea computer program containing one or more sequences of machine-readableinstructions describing methods of measuring targets on a substrateand/or analyzing measurements to obtain information about a lithographicprocess.

Although specific reference may have been made above to the use ofembodiments of the invention in the context of optical lithography, itwill be appreciated that the invention may be used in otherapplications, for example imprint lithography, and where the contextallows, is not limited to optical lithography. In imprint lithography atopography in a patterning device defines the pattern created on asubstrate. The topography of the patterning device may be pressed into alayer of resist supplied to the substrate whereupon the resist is curedby applying electromagnetic radiation, heat, pressure or a combinationthereof. The patterning device is moved out of the resist leaving apattern in it after the resist is cured.

The terms “radiation” and “beam” used herein encompass all types ofelectromagnetic radiation, including ultraviolet (UV) radiation (e.g.,having a wavelength of or about 365, 355, 248, 193, 157 or 126 nm) andextreme ultra-violet (EUV) radiation (e.g., having a wavelength in therange of 5-20 nm), as well as particle beams, such as ion beams orelectron beams.

The term “lens”, where the context allows, may refer to any one orcombination of various types of optical components, includingrefractive, reflective, magnetic, electromagnetic and electrostaticoptical components.

The embodiments may further be described using the following clauses:

1. A method of characterizing a distortion in a lithographic process,said method comprising:

obtaining measurement data corresponding to a plurality of measurementlocations on a substrate, said measurement data comprising measurementsperformed on a plurality of substrates, and comprising one or moremeasurements performed on one or more of said substrates for each ofsaid measurement locations;

determining for each of said measurement locations a first quality valuerepresenting a quality metric and a noise value representing a noisemetric from the measurements performed at that measurement location;

determining a plurality of distortion parameters, each distortionparameter being configured to characterize a systematic distortion insaid quality metric;

determining a statistical significance of said distortion parametersfrom said first quality value and from said noise value; and

parameterizing the systematic distortion from the distortion parametersdetermined to be statistically significant.

2. A method according to clause 1, further comprising a step ofdetermining corrections for a lithographic process based on aparameterization resultant from the parameterizing step.

3. A method according to clause 2, further comprising a step ofperforming a lithographic process using said corrections.

4. A method according to any preceding clause, wherein said measurementdata comprises measurements performed on a subset of a preselected setof measurement locations on each substrate, the subset being varied fordifferent substrates.

5. A method according to clause 4, wherein the subset for each substrateis selected according to an order of the measurement locations.

6. A method according to clause 4, wherein the subset for each substrateis selected randomly or pseudo-randomly.

7. A method according to clause 4, 5 or 6, wherein said subset isselected to optimize the number of distortion parameters which can bedetermined with statistical significance.

8. A method according to any preceding clause, wherein said qualitymetric is an overlay metric being a measure of unintentional positionaloffset between different layers on the substrate.

9. A method according to any of clauses 1 to 7, wherein said qualitymetric is any one selected from a list comprising: critical dimension,focus or dose.

10. A method according to any preceding clause, wherein said firstquality value comprises an average of actual measurements of the qualitymetric at each location.

11. A method according to any preceding clause, wherein said noise valuecomprises a random variation in different measurements performed at eachmeasurement location.

12. A method according to clause 11, wherein said noise value comprisesan average of the random variation in actual measurements of the firstquality value at each location.

13. A method according to any preceding clause, wherein the step ofparameterizing comprises selecting a distortion parameter model from anumber of distortion parameter models.

14. A method according to any of clauses 1 to 12, wherein the step ofparameterizing comprises parameterizing determined on a singledistortion parameter basis.

15. A method according to any preceding clause, wherein the step ofparameterizing comprises parameterizing based on a number of distortionparameters varying between a minimum number less than 100 and a maximumnumber greater than 1000.

16. A method according to any preceding clause, wherein said distortionparameters are parameters of one or more models.

17. A method according to any preceding clause, comprising, for each ofsaid measurement locations:

determining a second quality value representing the quality metric usinga lower resolution model;

determining a difference between the first quality value and the secondquality value; and

determining whether the difference is statistically significant.

18. A method according to clause 17, wherein the step of parameterizingfurther comprises, for each measurement location, including a greaternumber of distortion parameters for the parameterizing the systematicdistortion when said difference is determined to be statisticallysignificant compared to when the difference is determined to be notstatistically significant or when there is no difference.

19. A method according to clause 18, wherein:

the systematic distortion in said quality metric is characterized by thedistortion parameters defined by a higher resolution model when saiddifference is statistically significant, and by a lower resolution modelwhen said difference is not statistically significant or when there isno difference.

20. A method according to clause 19, wherein said lower resolution modelcomprises a polynomial for fitting the measurements.

21. A method according t any of clauses 17 to 20, wherein said step ofdetermining whether the difference is statistically significantcomprises:

determining a confidence interval for each of first quality values usingsaid noise values; and

determining said difference is statistically significant when saiddifference is outside of said confidence interval.

22. A method according to any preceding clause, comprising performingsaid method iteratively with said measurement data comprising a greaternumber of measurements at each iteration.

23. A method according to clause 22, comprising, for one or moredistortion parameters determined not to be statistically significant bya small margin, measuring a measurement location corresponding to thesedistortion parameters during a next iteration.

24. A method according to clause 23, wherein said small margin isdefined as being within 30% of a corresponding confidence interval.

25. A method according to clause 23, wherein said small margin isdefined as being within 10% of a corresponding confidence interval.

26. A method according to any of clauses 22 to 25, wherein saidplurality of substrates are divided into lots and each iteration isperformed for a different lot of substrates.

27. A method according to any preceding clause, comprising performingsaid measurements at a plurality of measurement locations on a pluralityof substrates to obtain said measurement data.

28. A computer program comprising processor readable instructions which,when run on suitable processor controlled apparatus, cause the processorcontrolled apparatus to perform the method of any preceding clause.

29. A computer program carrier comprising the computer program of clause28.

30. A lithographic apparatus being operable to perform the method of anyof clauses 1 to 26.

31. A lithographic apparatus according to clause 30, comprising:

an illumination optical system arranged to illuminate a pattern;

a projection optical system arranged to project an image of the patternonto a substrate.

32. A lithographic cell comprising the lithographic apparatus of clause30 or 31 and a metrology apparatus, said lithographic cell beingoperable to perform the method of clause 27.

The foregoing description of the specific embodiments will so fullyreveal the general nature of the invention that others can, by applyingknowledge within the skill of the art, readily modify and/or adapt forvarious applications such specific embodiments, without undueexperimentation, without departing from the general concept of thepresent invention. Therefore, such adaptations and modifications areintended to be within the meaning and range of equivalents of thedisclosed embodiments, based on the teaching and guidance presentedherein. It is to be understood that the phraseology or terminologyherein is for the purpose of description by example, and not oflimitation, such that the terminology or phraseology of the presentspecification is to be interpreted by the skilled artisan in light ofthe teachings and guidance.

The breadth and scope of the present invention should not be limited byany of the above-described exemplary embodiments, but should be definedonly in accordance with the following claims and their equivalents.

The invention claimed is:
 1. A method of characterizing a distortion ina lithographic process, the method comprising: obtaining measurementdata corresponding to a plurality of measurement locations on asubstrate, the measurement data comprising measurements performed on aplurality of substrates, and comprising one or more measurementsperformed on one or more of the substrates for each of the measurementlocations; determining, for each of the measurement locations, a firstquality value representing a quality metric and a noise valuerepresenting a noise metric from the one or more measurements performedat that respective measurement location; determining a plurality ofdistortion parameters, each distortion parameter configured tocharacterize a systematic distortion in the quality metric; determininga statistical significance of the distortion parameters from the firstquality value and from the noise value; and parameterizing thesystematic distortion from the distortion parameters determined to bestatistically significant.
 2. The method as claimed in claim 1, furthercomprising determining corrections for a lithographic process based on aparameterization resultant from the parameterizing.
 3. The method asclaimed in claim 2, further comprising performing a lithographic processusing the corrections.
 4. The method as claimed in claim 1, wherein themeasurement data comprises measurements performed on a subset of apreselected set of measurement locations on each substrate, the subsetbeing varied for different substrates.
 5. The method as claimed in claim4, wherein the subset for each substrate is selected according to anorder of the measurement locations, or wherein the subset for eachsubstrate is selected randomly or pseudo-randomly, or wherein the subsetis selected to optimize the number of distortion parameters which can bedetermined with statistical significance.
 6. The method as claimed inclaim 1, wherein the quality metric is an overlay metric, the overlaymetric being a measure of unintentional positional offset betweendifferent layers on the substrate.
 7. The method as claimed in claim 1,wherein the quality metric is any one selected from: critical dimension,focus or dose.
 8. The method as claimed in claim 1, wherein the firstquality value comprises an average of actual measurements of the qualitymetric at each location.
 9. The method as claimed in claim 1, whereinthe parameterizing comprises selecting a distortion parameter model froma number of distortion parameter models, or comprises parameterizingdetermined on a single distortion parameter basis, or comprisesparameterizing based on a number of distortion parameters varyingbetween a minimum number less than 100 and a maximum number greater than1000.
 10. The method as claimed in claim 1, wherein the distortionparameters are parameters of one or more models.
 11. The method asclaimed in claim 1, further comprising, for each of the measurementlocations: determining a second quality value representing the qualitymetric using a lower resolution model; determining a difference betweenthe first quality value and the second quality value; and determiningwhether the difference is statistically significant.
 12. The method asclaimed in claim 11, wherein the determining whether the difference isstatistically significant comprises: determining a confidence intervalfor each of first quality values using the noise values; and determiningthe difference is statistically significant when the difference isoutside of the confidence interval.
 13. The method as claimed in claim1, further comprising performing the method iteratively with themeasurement data comprising a greater number of measurements at eachiteration.
 14. The method as claimed in claim 13, further comprising,for one or more distortion parameters determined not to be statisticallysignificant by a certain margin, measuring a measurement locationcorresponding to these one or more distortion parameters during a nextiteration.
 15. A non-transitory computer program product comprisingprocessor readable instructions which, when run on a suitable processorcontrolled apparatus, cause the processor controlled apparatus to atleast: obtain measurement data corresponding to a plurality ofmeasurement locations on a substrate, the measurement data comprisingmeasurements performed on a plurality of substrates, and comprising oneor more measurements performed on one or more of the substrates for eachof the measurement locations; determine, for each of the measurementlocations, a first quality value representing a quality metric and anoise value representing a noise metric from the one or moremeasurements performed at that respective measurement location;determine a plurality of distortion parameters, each distortionparameter configured to characterize a systematic distortion in thequality metric; determine a statistical significance of the distortionparameters from the first quality value and from the noise value; andparameterize the systematic distortion from the distortion parametersdetermined to be statistically significant.
 16. The computer programproduct of claim 15, wherein the instructions are further configured tocause the processor controlled apparatus to determine corrections for alithographic process based on a parameterization resultant from theparameterizing the systematic distortion.
 17. The computer programproduct of claim 15, wherein the measurement data comprises measurementsperformed on a subset of a preselected set of measurement locations oneach substrate, the subset being varied for different substrates. 18.The computer program product of claim 15, wherein the quality metric isany one selected from: overlay, critical dimension, focus or dose. 19.The computer program product of claim 15, wherein the first qualityvalue comprises an average of actual measurements of the quality metricat each location.
 20. The computer program product of claim 15, whereinthe parameterization of the systematic distortion comprises selection ofa distortion parameter model from a number of distortion parametermodels, or comprises parameterization determined on a single distortionparameter basis, or comprises parameterization based on a number ofdistortion parameters varying between a minimum number less than 100 anda maximum number greater than 1000.